Question 74
If $$x - 2$$ is a common factor of $$x^3 — 4x^2 + ax + b, x^3 — ax^2 + bx + 8$$ then find the values of $$a$$ and $$b$$, respectively?
Solution
If x-2 is a common factor to both the expressions, then x= 2 is a root for both the equations.
By substituting value of x, we get:
$$2^3-4\cdot2^2+2a+b=0$$ ==> 2a+b = 8
$$2^3-a\cdot2^2+2b+8=0$$ ==> 2b-4a = -16 ==> 2a - b = 8
Adding both equations, we get 4a = 16 ==> a = 4 and b = 0.
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